Question

If you are driving and spot an object down the road, the distance it will take to stop is determined by the sum of these two functions:

Reaction Time: R(s) = 2.2s
Braking time: B(s) = 0.06392s
where s is the driving speed. Find the equation of the new function, D(s), that describes the distance it will take you to stop. If you see a deer in the road and are going 60mph, what is the distance it will take you to stop before hitting the deer?
a) D(s) = 2.2s + 0.06392s
b) D(s) = 2.2s - 0.06392s
c) D(s) = 2.2s * 0.06392s
d) D(s) = 2.2s / 0.06392s
(For the second part, provide a descriptive explanation.)

Answer 1

The equation for the stopping distance function is D(s) = 2.2s + 0.06392s, and using a speed of 60 mph, the stopping distance is approximately 60.6725 meters.

Step-by-step explanation:

To determine the stopping distance for a vehicle when an object is spotted on the road, we must consider both the reaction time and the braking time. The equation for the new function that describes the distance it will take to stop, denoted as D(s), is the sum of the reaction time function R(s) = 2.2s and braking time function B(s) = 0.06392s, where s represents the driving speed. Therefore, the correct equation is D(s) = R(s) + B(s) = 2.2s + 0.06392s, which matches option (a).

When the driver is travelling at a speed of 60 mph, which is approximately 26.8 meters per second (since 1 mile per hour is approximately 0.44704 meters per second), we substitute this value into the function to calculate the distance needed to stop:

D(26.8) = 2.2(26.8) + 0.06392(26.8) = 58.96 + 1.7125 ≈ 60.6725 meters.

Therefore, at a speed of 60 mph, the distance it will take to stop before hitting the deer is approximately 60.6725 meters.